A serializer is configured to generate a serialized signal for transmission across a channel between a transmitter and a receiver. The transmitter employs an encoding scheme to transmit symbols to the receiver across the channel. An example encoding scheme is a 2-level pulse amplitude modulation (PAM) scheme (PAM-2), which is also referred to as a non-return-to-zero (NRZ) scheme. For the NRZ scheme, the transmitted symbols have normalized signal levels of +1 and −1, where each symbol encodes a single bit. As data rates increase to meet demand for higher throughput, transmitters employ more than 2-level PAM schemes, where each symbol encodes more than one bit. For example, a PAM-4 scheme transmits symbols that have normalized signal levels of −3, −1, +1, and +3, where each symbol encodes two bits.
Conventional statistical analysis of the channel for NRZ may include modeling channel errors with a Gaussian probability distribution function. However, a Gaussian probability distribution function may not hold true for PAM-4. For example, in PAM-4, a Gaussian probability distribution function would predict more 1-level errors than 2-level errors. However, a systematic design issue in the system can cause more 2-level errors than 1-level errors. Alternatively, the upper two levels may exhibit more errors than the lower two levels, or the outer levels may exhibit more errors than the inner levels, due to design mismatch. Further, the conventional bit error rate (BER) analysis is insufficient to provide specific information for the distribution of errors in PAM-4 signaling.